IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v29y2006i2p417-422.html
   My bibliography  Save this article

A numerical analysis of chaos in the double pendulum

Author

Listed:
  • Stachowiak, Tomasz
  • Okada, Toshio

Abstract

We analyse the double pendulum system numerically, using a modified mid-point integrator. Poincaré sections and bifurcation diagrams are constructed for certain, characteristic values of energy. The largest Lyapunov characteristic exponents are also calculated. All three methods confirm the passing of the system from the regular low-energy limit into chaos as energy is increased.

Suggested Citation

  • Stachowiak, Tomasz & Okada, Toshio, 2006. "A numerical analysis of chaos in the double pendulum," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 417-422.
    • Handle: RePEc:eee:chsofr:v:29:y:2006:i:2:p:417-422
    DOI: 10.1016/j.chaos.2005.08.032
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905006703
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.08.032?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chu, Yan-Dong & Chang, Ying-Xiang & Zhang, Jian-Gang & Li, Xian-Feng & An, Xin-Lei, 2009. "Full state hybrid projective synchronization in hyperchaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1502-1510.
    2. Zhang, Jian-Gang & Li, Xian-Feng & Chu, Yan-Dong & Yu, Jian-Ning & Chang, Ying-Xiang, 2009. "Hopf bifurcations, Lyapunov exponents and control of chaos for a class of centrifugal flywheel governor system," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2150-2168.
    3. Lazare Osmanov & Ramaz Khomeriki, 2022. "Regular and chaotic motion of two bodies swinging on a rod," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(11), pages 1-7, November.
    4. Jiatong Chen & Bin Bao & Jinlong Liu & Yufei Wu & Quan Wang, 2022. "Pendulum Energy Harvesters: A Review," Energies, MDPI, vol. 15(22), pages 1-26, November.
    5. Liu, Zeyi & Rao, Xiaobo & Gao, Jianshe & Ding, Shunliang, 2023. "Non-quantum chirality and periodic islands in the driven double pendulum system," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    6. Machado, J. A. Tenreiro & Lopes, António M., 2016. "The N-link pendulum: Embedding nonlinear dynamics into the multidimensional scaling method," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 130-138.
    7. An, Xin-Lei & Yu, Jian-Ning & Chu, Yan-Dong & Zhang, Jian-Gang & Zhang, Li, 2009. "Global chaos synchronization of three coupled nonlinear autonomous systems and a novel method of chaos encryption," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 865-873.
    8. Coronel-Escamilla, A. & Gómez-Aguilar, J.F. & López-López, M.G. & Alvarado-Martínez, V.M. & Guerrero-Ramírez, G.V., 2016. "Triple pendulum model involving fractional derivatives with different kernels," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 248-261.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:29:y:2006:i:2:p:417-422. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.